Hochschild cohomology of algebras of differential operators tangent to a central arrangement of lines
Abstract
Given a central arrangement of lines $\mathcal{A}$ in a $2$-dimensional vector space $V$ over a field of characteristic zero, we study the algebra $\mathcal D(\mathcal A)$ of differential operators on $V$ which are logarithmic along $\mathcal A$. Among other things we determine the Hochschild cohomology of $\mathcal D(\mathcal A)$ as a Gerstenhaber algebra, establish a connection between that cohomology and the de Rham cohomology of the complement $M(\mathcal A)$ of the arrangement, determine the isomorphism group of $\mathcal D(\mathcal A)$ and classify the algebras of that form up to isomorphism.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2018
- DOI:
- 10.48550/arXiv.1807.10372
- arXiv:
- arXiv:1807.10372
- Bibcode:
- 2018arXiv180710372K
- Keywords:
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- Mathematics - K-Theory and Homology;
- 16E40;
- 14N20
- E-Print:
- 40 pages